We show that repeated-root cyclic codes over a finite chain ring are in general not
principally generated. Repeated-root negacyclic codes are principally generated if the
ring is a Galois ring with characteristic a power of 2. For any other finite chain ring
they are in general not principally generated. We also prove results on the structure,
cardinality and Hamming distance of repeated-root cyclic and negacyclic codes over a
finite chain ring.